The Orlicz-Brunn-Minkowski theory was introduced by Lutwak, Yang, and Zhang in 2010 and represents the latest substantially developed extension of the classical Brunn-Minkowski theory. The talk will be a survey on the current state of the new theory and its significance, with some thoughts about possible future extensions. I will spend some time giving the background, illustrated with a few pictures, for those who are not familiar with the Brunn-Minkowski theory. My own contribution is contained in joint work with Daniel Hug and Wolfgang Weil and with Deping Ye of the University of Newfoundland.